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Performance Gain of Full Duplex over Half Duplex
under Bidirectional Traffic Asymmetry
Juan Liu, Shengqian Han, Wenjia Liu
Beihang University, Beijing, China
Email: {liujuan, sqhan, liuwenjia}@buaa.edu.cn
Yong Teng, Naizheng Zheng
Nokia Networks, Beijing, China
Email: {yong.teng, naizheng.zheng}@nokia.com
Abstract—Recent work has demonstrated the advantage of
full-duplex (FD) network over half-duplex (HD) network in
bidirectional sum rate under the assumption of full-buffer and
symmetric uplink-downlink traffics. In this paper, we consider
asymmetric bidirectional traffics, and study the performance gain
of FD network over both the traditional time-division duplex
(TDD) network with static time slot splitting for uplink and
downlink and the dynamic TDD with adaptive time slot splitting
according to bidirectional traffics requirements. We use the
number of users supported by the networks as performance
metric, which is defined as the minimum of the number of
users supported in uplink and downlink given random data rate
requirements of users. To maximize the number of supported
users, bidirectional time slot splitting is optimized for dynamic
TDD network, and bidirectional power control at both BSs and
users is optimized in FD network. Numerical results show the
evident gain of FD network over traditional TDD for different
levels of traffic asymmetry, and the gain over dynamic TDD
decreases with the increase of traffic asymmetry.
I. INT ROD UC TI ON
Network densification with small cells in the fifth-
generation cellular systems (5G) significantly increases the
variation in traffic loads between different cells [1]. Moreover,
time-varying traffic asymmetry for uplink and downlink within
each cell is expected due to the proliferation of diverse appli-
cations for smart wireless devices, users’ mobility behaviour
and application usage behaviour, etc. Therefore, technologies
to deal with the spatio-temporally evolving bidirectional traffic
asymmetry are needed in 5G [2].
Frequency division duplex (FDD) systems are generally rec-
ognized as difficult to handle bidirectional traffic asymmetry
because of the equally paired frequency usage in downlink and
uplink. Asymmetrical FDD carrier aggregation by using more
frequency bands in one direction can solve the problem to a
certain extent, which however requires more transceivers at
users, leading to increased cost and power consumption [2].
By contrast, time division duplex (TDD) systems have the
capability to handle asymmetric bidirectional traffics. In tra-
ditional macro cell deployment scenarios, an asymmetric time
slot configuration can be employed for uplink and downlink,
which however needs to be used in all cells across the entire
network in order to avoid the detrimental opposite-directional
interference, e.g., the interference generated by a downlink
This work was supported in part by Nokia Networks, Beijing, China and
by the National Natural Science Foundation of China (No. 61301084).
transmitting base station (BS) to an uplink receiving BS.
The synchronous time slot configuration is highly inefficient
in small cell networks because of the spatio-temporal traffic
asymmetry, which motivates the investigation of cell-specific
dynamic TDD technology [3, 4]. The mitigation of opposite-
directional interference is a key challenge for dynamic TDD,
and various interference control methods have been proposed
in the literature, such as power control [5], access management
[6], coordinated beamforming [7], and cell clustering [1, 8].
Full duplex (FD) communication can be regarded as an
enhanced dynamic TDD in the sense that both uplink and
downlink in each cell operate simultaneously so that time
slot splitting is no longer necessary, which therefore can
naturally support the requirements of asymmetric bidirectional
traffics. FD communication was long believed impossible in
wireless system design due to the severe self-interference
within the same transceiver. However, the plausibility of FD
technique was approved by recent tremendous progress in self-
interference cancellation, and nearly doubled link performance
over the half duplex (HD) system was demonstrated for short-
range point-to-point communications [9,10]. The performance
of FD network has also been analyzed based on stochastic
geometry in [11–14], where evident gain in bidirectional sum
rate over the traditional HD network was shown when self-
interference in FD nodes is well controlled. However, the
existing analysis on the advantages of FD network is based
on the assumption either explicitly or implicitly that both BSs
and users have full buffer traffic and uplink-downlink traffics
are symmetric, e.g., in [12].
In this paper, we investigate the performance gain of FD
network over HD network including both traditional TDD
and dynamic TDD, where bidirectional traffic asymmetry is
considered. To maximize the number of users supported by
the networks, which is defined as the minimum of the number
of users supported in uplink and downlink, bidirectional time
slot splitting is optimized for dynamic TDD network, and
bidirectional power control at both BSs and users is optimized
in FD network for time division multiple access (TDMA)
and frequency division multiple access (FDMA), respectively.
Numerical results show that under asymmetric bidirectional
traffics, both FD network and dynamic TDD network exhibit
large performance gain over the traditional static TDD network
with equal time slot splitting, and the gain of FD network over
IEEE ICC2016-Workshops: W05-Workshop on Novel Medium Access and Resource Allocation for 5G Networks
978-1-5090-0448-5/16/$31.00 ©2016 IEEE
dynamic TDD network decreases with the increase of traffic
asymmetry.
II. SY ST EM MO DE L
Consider a small cell network consisting of multiple geo-
graphically separated cell clusters, which can be formed based
on the existing cell clustering methods designed for dynamic
TDD, e.g., [8]. Assume that the interference between cell
clusters is negligible as in [1], so that cluster-specific uplink-
downlink resource configuration can be employed based on the
bidirectional traffic requirements in each cluster, and different
configurations can be used between clusters. Within each
cluster, following the stochastic geometry model in [11], the
location of BSs follows a homogeneous Poisson point process
(PPP) Ψwith density λin the Euclidean plane, and the
uplink users served in the same time-frequency resource are
distributed according to an independent homogeneous PPP Ω
with the same density λ. In the paper, both FD and HD BSs
are respectively considered, but the users are in HD mode
due to the difficulty of implementing FD at user side. We
consider that each BS serves multiple users in TDMA or
FDMA manner. Then, on the same time-frequency resource a
HD BS can serve one uplink or downlink user, while a FD BS
can serve an uplink user and a downlink user simultaneously,
where every user is associated with its closest BS.
In FD network, the downlink transmission experiences the
interference from both other-cell BSs and all co-scheduled
uplink users. Based on the results in [11], the average downlink
data rate can be expressed as
¯
Rdf (Pb, Pu, W ) = 2πW0λ·(1)
Zr>0
re−λπr2Zt>0
e−rαbu (et−1)N0W0
PbF1f(r, t)F2f(r, t)dtdr,
where F1f(r, t) = e
−πλr2(et
−1)
2
αbu R∞
(et
−1)
−2/αbu
1
1+xαbu/2dx,
F2f(r, t) = e−πλr
2αbu
αuu PuW0(et−1)
PbW2/αuu Ry>0
1
1+yαuu/2dy ,
αbu and αuu denote the pathloss exponents between BSs
and users and between users, respectively, W0and Wdenote
the whole bandwidth and the bandwidth allocated to each
uplink user, respectively, Pband Puare the transmit powers of
BSs and users, respectively, N0is the noise power spectrum
density, and Rayleigh fading is considered for small-scale
channels. Herein, flat transmit power spectrum is considered
for both BSs and users, which is Pb
W0and Pu
W, respectively.
The uplink transmission in FD network suffers from the
inter-cell interference generated by both other-cell uplink users
and other-cell BSs, and also the self-interference from itself.
The average uplink data rate can be expressed as [11]
¯
Ruf (Pb, Pu, W )=2πW0λ·(2)
Zr>0
re−λπr2
Zt>0
e
−rαbu (et
−1)(N0W0
+βPb)W
PuW0F1f(r, t)F0
2f(r, t)dtdr,
where F0
2f(r, t) = e−πλr
2αbu
αbb PbW(et−1)
PuW02/αbb Ry>0
1
(1+yαbb/2)dy ,
αbb denotes the pathloss exponent between BSs, and β < 1
reflects the level of self-interference cancellation.
From the average data rates in FD network, we can easily
obtain the average data rates in HD network. Specifically,
define Tdand Tuas the fractions of time slots allocated to
downlink and uplink in TDD networks with Td+Tu= 1.
Then, the average downlink rate in HD network can be denoted
by Td¯
Rdh(Pb), where ¯
Rdh(Pb)can be obtained from (1) by
setting the transmit power of users as zeros, i.e., Pu= 0,
which leads to F2f(r, t)=1and ¯
Rdh(Pb)is independent of
W. Similarly, the average uplink rate in HD network can be
denoted by Tu¯
Ruh(Pu), where ¯
Ruh(Pu)can be obtained from
(2) by setting the transmit power of BSs as zeros, i.e., Pb= 0,
which leads to F0
2f(r, t)=1and disappeared self-interference.
In the paper we focus on the interference-limited scenario,
where both BSs and users have minimal transmit powers,
denoted by Pb,min and Pu,min, which ensure that the noise is
negligible compared to the inter-cell interference. By setting
N0= 0 in (1) and (2), we can find that the bidirectional
average data rates in FD network only depend on the ratio
of transmit power of BSs and users, defined as κ=Pb
Pu.
Specifically, the bidirectional average data rates in FD and
HD TDD networks in interference-limited scenario can be
obtained as
ˆ
Ruf (κ, W )=2πW0λ·(3a)
Zr>0
re−λπr2Zt>0
e
−rαbu (et
−1)βκW
W0F1f(r, t)F0
2f(r, t, κ, W )dtdr,
ˆ
Rdf (κ, W )=2πW0λ·(3b)
Zr>0
re−λπr2Zt>0
F1f(r, t)F2f(r, t, κ, W)dtdr,
ˆ
Ruh(Tu) = Tuˆ
Rh0,ˆ
Rdh(Td) = Tdˆ
Rh0,(3c)
where ˆ
Rh0= 2πW0λRr>0re−λπr2Rt>0F1f(r, t)dtdr.
We can observe from (3) that the bidirectional average data
rates in FD network depend on both power ratio, κ, and
bandwidth allocated to each uplink user, W, which means that
the performance of FD network will be different under TDMA
and FDMA. By contrast, in HD network the bidirectional
average rates only depend on the time slot splitting, meaning
that multiple accessing strategies have no impact on the
performance.
III. RESOURCE CON FIG UR ATIO N UN DE R BIDIRECTIONAL
TRA FFIC AS YM ME TRY
A. Performance Metric
In the paper we use the number of users supported by a
network, K, as the performance metric, which is defined as
the minimum of the number of users supported in uplink, Ku,
and downlink, Kd, i.e., K= min(Ku, Kd). The values of Ku
and Kddepend on the bidirectional traffic requirements. To
model the asymmetric bidirectional traffics, we assume that
the data rate requirements of all users in either direction are
independent and identically distributed (i.i.d.), but no specific
distributions are assumed. Let Rui and Rdj denote the data rate
requirements of an arbitrary uplink user iand downlink user
j, which have the means, muand md, and variances, σ2
uand
σ2
d, respectively. With the random rate requirements, we define
Kuand Kdas the number of users that can be supported in
uplink and downlink with the probability no less than a given
value , respectively, where the value of is generally large,
e.g., = 95%.
B. HD Network
In this subsection we optimize the resource configuration
for HD dynamic TDD network. The optimization problem,
aimed at maximizing the number of supported users under
asymmetric bidirectional traffics, can be formulated as
max
Tu+Td=1 K=min(Ku, Kd)(4a)
s.t. PPKu
i=1Rui ≤Tuˆ
Rh0≥(4b)
PPKd
j=1Rdj ≤Tdˆ
Rh0≥, (4c)
where P{·} denotes the probability.
To solve problem (4), we observe that P{·} is a decreasing
function for both Kuand Kd, therefore for any given Tuand
Tdthe optimal solution can be obtained when constraint (4b)
and (4c) hold with equality.1Moreover, we can find from (4b)
and (4c) that Kuis an increasing function of Tu, while Kdis
a decreasing function of Tu. Therefore, in order to maximize
the minimum of Kuand Kd, i.e., Kin (4a), the optimal Tu
should be selected to make Ku=Kd=K. As a result,
problem (4) can be equivalently transformed as
max
Tu+Td=1 K(5a)
s.t. PPK
i=1Rui ≤Tuˆ
Rh0=(5b)
PPK
j=1Rdj ≤Tdˆ
Rh0=. (5c)
To solve problem (5), we first find explicit expressions for
constraint (5b) and (5c). Considering that the number of uplink
and downlink users supported in current and future networks
is generally large, we can employ the central limit theorem to
simplify the constraints. Take constraint (5b) as an example,
which can be transformed as
PPK
i=1Rui ≤Tuˆ
Rh0= ΦTuˆ
Rh0−Kmu
σu√K=, (6)
where the first equality follows from central limit theorem,
and Φ(·)is the cumulative distribution function (CDF) of
the standard Gaussian distribution with zero mean and unit
variance. Letting Φ−1(·)denote the inverse function of Φ(·),
we can rewrite problem (4) as
max
Tu+Td=1 K(7a)
s.t. Kmu+ Φ−1()σu√K=Tuˆ
Rh0(7b)
Kmd+ Φ−1()σd√K=Tdˆ
Rh0.(7c)
From (7), the optimal K∗can be solved as
K∗=−Φ−1()σud +qΦ−2()σ2
ud + 4mud ˆ
Rh02
4m2
ud
,(8)
1Throughout the paper we consider that the numbers of users, Kuand Kd,
are continuous variables, and the integer constraints on Kuand Kdcan be
easily included by using floor operation to the obtained continuous values.
where σud ,σu+σdand mud ,mu+md.
From (7b) and (7c), we can obtain that the optimal time
slot splitting, T∗
uand T∗
d, satisfy
T∗
u
T∗
d
=mu·√K∗+ Φ−1()σu
mu
md·√K∗+ Φ−1()σd
md.(9)
Under a special case with σu
mu=σd
md, i.e., the standard
deviation of data rate requirement is proportional to the
average data rate requirement for both directions, we can
obtain from (9) that
T∗
u
T∗
d
=mu
md
.(10)
It is shown that in this case the time slots configured
to uplink and downlink are proportional to the bidirectional
average data rate requirements. An example for this special
case is when the data rate requirements of users follow
exponential distribution with mean muand mdfor uplink
and downlink, respectively, where the corresponding standard
deviations are σu=muand σd=md.
C. FD Network
In this subsection the resource configuration is optimized for
FD network, which has two differences from the optimization
of HD network. First, in FD network both uplink and downlink
use all time-frequency resources, and the power ratio of BSs
and users, i.e., κ, needs to be optimized instead of time
slot splitting. Second, as mentioned before, the bidirectional
performance in FD network depends on the bandwidth allo-
cated to each uplink user, W, which is different in TDMA
and FDMA networks. Therefore, the optimizations for FD
TDMA and FDMA networks are considered, respectively, in
the following.
1) FD Network with TDMA: In TDMA network each
uplink user can use full bandwidth, i.e., W=W0. Then, the
uplink and downlink average data rates in FD network given
in (3a) and (3b) only depend on the power ratio κ, which are
denoted by ˆ
Ruf (κ)and ˆ
Rdf (κ), respectively, for notational
simplicity.
To obtain the optimal Kin FD TDMA network, we can
solve problem (4) by replacing Tuˆ
Rh0in (4b) and Tdˆ
Rh0
in (4c) with ˆ
Ruf (κ)and ˆ
Rdf (κ), respectively. It is easy
to find that the optimal solution can be obtained when the
constraints in the resulting problem hold with equality. Then,
the optimization problem, aimed at maximizing the number of
supported users, can be formulated as
max
κK= min(Ku, Kd)(11a)
s.t. PPKu
i=1Rui ≤ˆ
Ruf (κ)=(11b)
PPKd
j=1Rdj ≤ˆ
Rdf (κ)=(11c)
κmin ≤κ≤κmax,(11d)
where κmin =Pb,min
Pu,max and κmax =Pb,max
Pu,min denote the lower
and upper bounds of power ratio κ, and Pb,max and Pu,max are
the maximal transmit powers of BSs and users, respectively.
To solve problem (11), noting that ˆ
Ruf (κ)is a decreasing
function of κand ˆ
Rdf (κ)is an increasing function of κ, we
can obtain from (11b) and (11c) that Kudecreases with κ
while Kdincreases with κ. Based on this result, the maximal
Kcan be found as follows.
First, omitting constraint (11d), we can find that the solu-
tions to the relaxed problem, denoted by ˜
K,˜
Ku,˜
Kdand ˜κ, are
obtained when ˜
Ku=˜
Kd=˜
K. By further applying the central
limit theorem as in HD network, the following equations are
satisfied
˜
Kmu+ Φ−1()σup˜
K=ˆ
Ruf (˜κ)(12a)
˜
Kmd+ Φ−1()σdp˜
K=ˆ
Rdf (˜κ),(12b)
from which the optimal ˜κ∗and ˜
K∗can be easily obtained by
a bisection method.
Then, recalling that Kdincreases with κand Kudecreases
with κ, if ˜κ∗> κmax , we have Ku> Kdfor all κ∈
[κmin, κmax ], so that K∗=Kd, which can be obtained from
(12b) by setting κ=κmax and ˜
K=K∗. On the other hand,
if ˜κ∗< κmin, we have Ku< Kdfor all κ∈[κmin, κmax ], so
that K∗=Ku, which can be obtained from (12a) by setting
κ=κmin and ˜
K=K∗. Otherwise, if ˜κ∗∈[κmin , κmax], we
have K∗=˜
K∗and κ∗= ˜κ∗.
2) FD Network with FDMA: When FDMA is considered,
the bandwidth allocated to each uplink user is W=W0
Ku, which
is a function of Ku. We can observe from (3a) and (3b) that
now the uplink and downlink average data rates of FD network
are determined by κ
Ku, which are denoted by ˆ
Ruf (κ
Ku)and
ˆ
Rdf (κ
Ku)for simplicity in FDMA network.
Similar to (4), the number of supported users can be
maximized as follows.
max
κK=min(Ku, Kd)(13a)
s.t. PPKu
i=1Rui ≤ˆ
Ruf (κ
Ku)≥(13b)
PPKd
j=1Rdj ≤ˆ
Rdf (κ
Ku)≥(13c)
κmin ≤κ≤κmax.(13d)
In the problems for HD dynamic TDD and FD TDMA
networks, Kuand Kdare constrained separately, e.g., in (4b)
and (4c), so that Kis maximized when Kuand Kdreach
their maximal values, respectively. In FD FDMA network,
Kdis constrained only in (13c), and thus the optimal Kcan
be obtained when Kdreaches its maximal value. For Ku,
however, since it is constrained in both (13b) and (13c), it is
not necessarily optimal to set Kuas its maximal value. Based
on the analysis, we can rewrite constraint (13b) and (13c) as
Ku≤Kmax
u(κ)(14a)
Kd=Kmax
d(κ
Ku
),(14b)
where Kmax
u(κ)and Kmax
d(κ
Ku)denote the maximal values
of Kuand Kdunder constraint (13b) and (13c), respectively.
Kmax
u(κ)and Kmax
d(κ
Ku)have the following properties.
Proposition 1: For any given κ,Kmax
u(κ)and Kmax
d(κ
Ku)
are obtained when constraint (13b) and (13c) hold with
equality, respectively. Moreover, Kmax
u(κ)is a decreasing
function of κ, and Kmax
d(κ
Ku)is an increasing function of
κ
Ku.
Proof: See Appendix A.
Based on Proposition 1 and the central limit theorem as
used in (6), the functions Kmax
u(κ)and Kmax
d(κ
Ku)can be
found from the following equations
Kmax
umu+ Φ−1()σupKmax
u=ˆ
Ruf (κ
Kmax
u
)(15a)
Kmax
dmd+ Φ−1()σdpKmax
d=ˆ
Rdf (κ
Ku
).(15b)
Since Kmax
d(κ
Ku)increases with κ
Kuaccording to Proposi-
tion 1 and further considering (14a) and (14b), we can rewrite
problem (13) as
max
κK=min(Ku, Kd)(16a)
s.t. Ku≤Kmax
u(κ)(16b)
Kd=Kmax
d(κ
Ku
)≥Kmax
d(κ
Kmax
u(κ))(16c)
κmin ≤κ≤κmax.(16d)
In order to maximize K=min(Ku, Kd)in problem (16), we
first investigate if the feasible regions of Kuand Kdoverlap.
If the regions overlap, then Kis maximized when Ku=Kd;
otherwise, Ku6=Kd. To this end, we need to compare the
upper bound of Ku, i.e., the term Kmax
u(κ)in (16b), and
the lower bound of Kd, i.e., the term Kmax
d(κ
Kmax
u(κ))in
(16c). Define ˜κas the solution to the equation Kmax
u(κ) =
Kmax
d(κ
Kmax
u(κ)),˜
K. By substituting ˜
Kand ˜κinto (15), we
have
˜
Kmu+ Φ−1()σup˜
K=ˆ
Ruf (˜κ
˜
K)(17a)
˜
Kmd+ Φ−1()σdp˜
K=ˆ
Rdf (˜κ
˜
K).(17b)
Since ˆ
Ruf (˜κ
˜
K)and ˆ
Rdf (˜κ
˜
K)are respectively decreasing and
increasing functions of ˜κ
˜
K, the value of ˜κcan be readily
computed with a bisection method.
According to Proposition 1, we know that Kmax
u(κ)de-
creases with κand Kmax
d(κ
Kmax
u(κ))increases with κ. There-
fore, if there exists κ≤˜κwithin its feasible region
[κmin, κmax ], then Kmax
u(κ)≥Kmax
d(κ
Kmax
u(κ))holds and
the feasible regions of Kuand Kdoverlap; otherwise, the
regions have no intersection. Based on the result, we next
solve problem (16) in two cases.
First, if κmin ≤˜κ, then there exists κ∈
[κmin,min(˜κ, κmax)] satisfying κ≤˜κ. In this case,
the feasible regions of Kuand Kdoverlap, and the
objective function of problem (16) is maximized when
K=Ku=Kd=Kmax
d(κ
Ku), where the final equality
comes from (16c). By substituting Ku=Kmax
d(κ
Ku)into
(15b), we obtain
Kmax
dmd+ Φ−1()σdpKmax
d=ˆ
Rdf (κ
Kmax
d
).(18)
Fig. 1. Bidirectional resource configuration in FD and HD dynamic TDD
networks v.s. md
mu.
Since ˆ
Rdf (·)is an increasing function, we know that Kmax
d
must increase with the growth of κ. This means that Kmax
d
is maximized when κreaches its maximum, i.e., the optimal
κ∗= min(˜κ, κmax ). Given κ∗, the maximal Kmax∗
dcan be
obtained with a bisection method from (18). Finally, we have
the optimal K∗
u=K∗
d=K∗=Kmax∗
d.
Second, if κmin >˜κ, we have Kmax
u(κ)<
Kmax
d(κ
Kmax
u(κ))for all κ∈[κmin, κmax ], i.e., the maximal
possible value of Kuis smaller than the minimal possible
value of Kd. Therefore, it is clear that the optimal K∗=
K∗
u=Kmax∗
u(κ∗), where Kmax∗
u(κ∗)can be solved from
(15a) by choosing the optimal κ∗=κmin because Kmax
u(κ)
decreases with κaccording to Proposition 1.
IV. NUMERICAL RES ULT S
In this section, we evaluate the performance of FD and
HD networks based on the proposed resource configuration
methods, and investigate the performance gain of FD network
over traditional static TDD and dynamic TDD networks. The
following system parameter setups are considered. The system
bandwidth is 10 MHz, the noise power spectrum density is
−174 dBm/Hz, and the noise figure is 9dB, from which
we can obtain the total noise power is −95 dBm [15]. The
density of BSs is set as λ=2×10−4m−2, which corresponds
to an average cell radius of 40 m. The pathloss for the
channels between BSs, between users, and between BSs and
users are calculated based on the Hata model [16], where
the heights of BSs and users are set as 10 m and 1.5m,
respectively. The maximal transmit powers of BSs and users
are Pb,max =23 dBm and Pu,max =23 dBm, respectively [15].
In order to ensure that the networks operate in interference-
limited scenario, the minimal transmit power of BSs, Pb,min
is selected to satisfy the condition ˆ
Rh0−¯
Rdh(Pb,min )
¯
Rdh(Pb,min )= 10−4
for HD static TDD network with Td=Tu, where ˆ
Rh0and
¯
Rdh are the average downlink rates in the cases without and
with noise as defined in Section II, respectively. This condition
means that the impact of ignoring noise on the average rate
Fig. 2. Performance gain of FD network over HD static TDD and dynamic
TDD networks v.s. md
mu.
should be very small. We can obtain that Pb,min =−5.2dBm,
and the minimal transmit power of users can be obtained in
the same way as Pu,min =−5.2dBm. Then, the range of
κcan be obtained as κmin = 0.0015 and κmax = 660.7.
The parameter reflecting the residual self-interference in FD
network is set as β=−110 dB. The data rate requirements of
users are modeled as exponential distribution with means mu
and mdfor uplink and downlink, respectively, where muis set
as 100 kbps and different values of mdwill be considered. The
probability value used for defining the number of supported
users is set as = 95%. In static TDD network, the time slots
are equally allocated to uplink and downlink.
Figure 1 shows the optimal bidirectional power control
for FD TDMA and FDMA networks and the optimal time
slot splitting in HD dynamic TDD network, as a function
of the ratio of average downlink rate requirement to average
uplink rate requirement, md
mu. It is shown that in FD network
downlink-to-uplink transmit power ratio, κ, increases with md
mu
as expected. For a given md
mu, a higher κis required by FDMA
network compared to TDMA network. This means that given
κ, i.e., given the transmit powers of BSs and users, TDMA
network can achieve high downlink rate and low uplink rate,
while FDMA network can achieve low downlink rate but high
uplink rate. This is because compared to TDMA network, in
FDMA network each user transmits within a narrow band in
uplink, which increases the power spectrum of desired signal
but also increases the interference to downlink users, where
the BS needs to spread the power over full bandwidth. The
result suggests that TDMA is suitable for the scenarios where
downlink traffic dominates, while FDMA is suitable for the
scenarios where uplink traffic dominates. Moreover, we can
observe that in FDMA network κkeeps constant when md
mu≥5,
which reaches the maximal κmax. Yet, for md
mu<5in FDMA
network and for any md
muin TDMA network, we can observe
from the two curves that κincreases proportionally with
qmd
mk. Such a scaling result can be proven theoretically, which
however is not provided in the paper due to lack of space. For
HD dynamic TDD network, we can see that the ratio of time
slots configured for downlink and uplink increases linearly
with md
mu, which coincides with our analysis in Section III-B.
Figure 2 depicts the performance relationship between FD
network and HD static TDD as well as dynamic TDD network-
s. It is shown that compared to the static TDD network, FD
network with TDMA and FDMA can improve the network
performance evidently. When symmetric bidirectional traffic
requirements are considered, in which case the static TDD
network operates optimally, the gain near 40% can be achieved
by FD network. When the bidirectional traffic requirements
are asymmetric, FD network can even achieve the gain up to
130% over the static TDD network. Moveover, in FD network
TDMA can achieve higher gain over FDMA when downlink
traffic dominates, which agrees with the analysis in Fig. 1. The
gain of FD network over dynamic TDD network decreases
with the growth of traffic asymmetry as expected. When
typical values of md
muranging from four to six are considered
[17], FD network can provide a gain of 10% ∼20% compared
to dynamic TDD network.
V. CONCLUSIONS
In this paper we investigated the performance gain of FD
network over HD network including both traditional static
TDD network and dynamic TDD network. We maximized
the number of supported users in FD TDMA and FDMA
networks as well as HD dynamic TDD network by optimizing
bidirectional power control and time slot splitting, respectively,
where asymmetric uplink-downlink traffic requirements were
taken into account. Numerical results showed that different
from HD network where multiple accessing strategy has no
impact on the maximal number of supported users, in FD
network TDMA is suitable for the scenarios where downlink
traffic dominates, while FDMA is suitable for the scenarios
where uplink traffic dominates. Under asymmetric bidirec-
tional traffics, both FD network and dynamic TDD network
exhibit evident performance gains over the traditional static
TDD network. Compared to dynamic TDD network, the gain
of FD network changes with the traffic asymmetry, and the
gain up to 20% can be achieved for the typical downlink traffic
dominant scenarios.
APPENDIX A
PROO F OF PROPOSITION 1
For downlink, it is obvious from (13c) that Kdis maximized
when (13c) holds with equality and increases with κ
Kubecause
ˆ
Rdf increases with κ
Ku.
For uplink, we prove the properties of Kuby contradiction.
Let Kmax
udenote the maximal value of Kuconstrained by
(13b). Assume that (13b) holds with strict inequality when
Ku=Kmax
u, i.e., PPKmax
u
i=1 Rui ≤ˆ
Ruf (κ
Kmax
u)> . Then,
we can always find a ˆ
Ku> Kmax
uso that PPˆ
Ku
i=1Rui ≤
ˆ
Ruf (κ
Kmax
u)=. Since ˆ
Ruf (κ
Ku)is a decreasing function
of Was shown in (3a) and hence is an increasing function
with Ku, we have PPˆ
Ku
i=1Rui ≤ˆ
Ruf (κ
ˆ
Ku)> . This
means that there exists a ˆ
Kuthat is larger than Kmax
uand
satisfies constraint (13b). This is contradictory with the fact
that Kmax
uis defined as the maximal value of Ku. Therefore,
the considered assumption is false, and Kuis maximized when
(13b) holds with equality.
We proceed to prove that Kmax
uis an increasing function
of κ. Define ¯
Kmax
uand ˆ
Kmax
uas the maximal number of
Kuwhen κequals to ¯κand ˆκ, respectively. Without loss of
generality, we set ˆκ > ¯κ. Then, we have =PPˆ
Kmax
u
k=1 Ruk ≤
ˆ
Ruf (ˆκ
ˆ
Kmax
u
)<PPˆ
Kmax
u
k=1 Ruk ≤ˆ
Ruf (¯κ
ˆ
Kmax
u
), where the
inequality comes from the fact that ˆ
Ruf (κ
Ku)decreases with
κ. The result shows that when κ= ¯κ,ˆ
Kmax
ucannot make
constraint (13b) hold with equality. It means that ˆ
Kmax
uis only
a feasible point, so that ˆ
Kmax
u<¯
Kmax
umust hold. Therefore,
Kmax
udecreases with κ.
REFERENCES
[1] Z. Shen, A. Khoryaev, E. Eriksson, and X. Pan, “Dynamic uplink-
downlink configuration and interference management in TD-LTE,” IEEE
Commun. Mag., vol. 50, no. 11, pp. 51–59, 2012.
[2] S. Chen and J. Zhao, “The requirements, challenges, and technologies
for 5G of terrestrial mobile telecommunication,” IEEE Commun. Mag.,
vol. 52, no. 5, pp. 36–43, 2014.
[3] A. Dowhuszko, O. Tirkkonen, J. Karjalainen, T. Henttonen, and
J. Pirskanen, “A decentralized cooperative uplink/downlink adaptation
scheme for TDD small cell networks,” in Proc. IEEE PIMRC, 2013.
[4] V. Venkatasubramanian, M. Hesse, P. Marsch, and M. Maternia, “On
the performance gain of flexible UL/DL TDD with centralized and
decentralized resource allocation in dense 5G deployments,” in Proc.
IEEE PIMRC, 2014.
[5] H. Lee and D.-H. Cho, “Combination of dynamic-TDD and static-TDD
based on adaptive power control,” in Proc. IEEE VTC-Fall, 2008.
[6] H. Sun, M. Sheng, M. Wildemeersch, and T. Quek, “Coverage analysis
for two-tier dynamic TDD heterogeneous networks,” in Proc. IEEE
GLOBECOM, 2014.
[7] P. Jayasinghe, A. Tolli, J. Kaleva, and M. Latva-aho, “Bi-directional
signaling for dynamic TDD with decentralized beamforming,” in Proc.
IEEE ICC Workshop, 2015.
[8] D. Zhu and M. Lei, “Cluster-based dynamic DL/UL reconfiguration
method in centralized RAN TDD with trellis exploration algorithm,”
in Proc. IEEE WCNC, 2013.
[9] M. Jain, J. Choi, T. Kim, D. Bharadia, S. Seth, K. Srinivasan, P. Levis,
S. Katti, and P. Sinha, “Practical, real-time, full duplex wireless,” in
Proc. ACM MOBICOM, 2011.
[10] M. Duarte, C. Dick, and A. Sabharwal, “Experiment-driven characteri-
zation of full-duplex wireless systems,” IEEE Trans. Wireless Commun.,
vol. 11, no. 12, pp. 4296–4307, 2012.
[11] S. Goyal, P. Liu, S. Hua, and S. Panwar, “Analyzing a full-duplex cellular
system,” in Proc. CISS, 2013.
[12] H. Alves, C. de Lima, P. Nardelli, R. Demo Souza, and M. Latva-aho,
“On the average spectral efficiency of interference-limited full-duplex
networks,” in Proc. CROWNCOM, 2014.
[13] J. Lee and T. Quek, “Hybrid full-/half-duplex system analysis in hetero-
geneous wireless networks,” IEEE Trans. Wireless Commun., vol. 14,
no. 5, pp. 2883–2895, 2015.
[14] Z. Tong and M. Haenggi, “Throughput analysis for full-duplex wireless
networks with imperfect self-interference cancellation,” IEEE Trans.
Commun., vol. 63, no. 11, pp. 4490–4500, 2015.
[15] 3GPP TR 36.814, “Further Advancements for E-UTRA Physical Layer
Aspects (Release 9),” 2010.
[16] A. Sadek and S. Shellhammer, “A unified path-loss model for
coexistence study,” 2008. [Online]. Available: https://mentor.ieee.org/
802.19/file/08/19-08-0006-00-0000-unified-path-loss-model.doc
[17] Report ITU-R M.2370, “IMT Traffic estimates for the years 2020 to
2030,” 2015.
